name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 686 | allowCompletion bool 2
classes |
|---|---|---|---|
WeierstrassCurve.valuation_Δ_aux.eq_1 | Mathlib.AlgebraicGeometry.EllipticCurve.Reduction | [
"WeierstrassCurve.Δ",
"Int.instAddCommMonoid",
"IsDomain",
"Multiplicative.linearOrder",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Int.instLinearOrder",
"IsFractionRing",
"IsDiscreteValuationRing",
"PartialOrder.toP... | true |
NonUnitalCommCStarAlgebra.rec | Mathlib.Analysis.CStarAlgebra.Classes | [
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CompleteSpace",
"NormedSpace",
"AddMonoid.toAddSemigroup",
"NonUnitalNonAssocRing.toMul",
"NonUnitalCommCStarAlgebra",
"AddCommGroup.toAddCommMonoid",
"IsScalarTower",
"NormedSpace.toModule",
"AddMonoid.toZero",
"NonUnitalNonAssocRing.toAddCommGr... | false |
AlgHom.liftOfSurjective._proof_4 | Mathlib.RingTheory.Ideal.Quotient.Operations | [
"CommRing",
"AlgHom.algHomClass",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"AlgHom.liftOfSurjective._proof_3",
"Algebra",
"Ideal.IsTwoSided",
"RingHom.instIsTwoSidedKer",
"CommRing.toCommSemiring",
"AlgHomClass.toRingHomClass",
"CommRing.toRing",
"Ring.toSemiring",
"RingHom.k... | false |
_private.Mathlib.RingTheory.HahnSeries.Multiplication.0.HahnModule.coeff_smul_right._simp_1_2 | Mathlib.RingTheory.HahnSeries.Multiplication | [
"Finset",
"Finset.instSDiff",
"Membership.mem",
"Finset.mem_sdiff",
"SDiff.sdiff",
"And",
"Finset.instSetLike",
"propext",
"Eq",
"Not",
"SetLike.instMembership",
"DecidableEq"
] | false |
HDiv.hDiv | Init.Prelude | [
"outParam",
"HDiv"
] | true |
Valuation.toMonoidWithZeroHom | Mathlib.RingTheory.Valuation.Basic | [
"NonAssocSemiring.toMulZeroOneClass",
"CommMonoidWithZero.toMonoidWithZero",
"LinearOrderedCommMonoidWithZero.toCommMonoidWithZero",
"MonoidWithZeroHom",
"MonoidWithZero.toMulZeroOneClass",
"LinearOrderedCommMonoidWithZero",
"Semiring.toNonAssocSemiring",
"Ring.toSemiring",
"Ring",
"Valuation"
] | true |
Lean.Meta.Grind.EMatch.SearchState._sizeOf_inst | Lean.Meta.Tactic.Grind.EMatch | [
"Lean.Meta.Grind.EMatch.SearchState",
"Lean.Meta.Grind.EMatch.SearchState._sizeOf_1",
"SizeOf.mk",
"SizeOf"
] | false |
_private.Mathlib.Tactic.Translate.Reorder.0.Mathlib.Tactic.Translate.guessReorder.visit._sparseCasesOn_11 | Mathlib.Tactic.Translate.Reorder | [
"Nat.ne_of_beq_eq_false",
"Lean.Expr.const",
"Lean.Expr.letE",
"Lean.Expr.mvar",
"Nat.shiftRight",
"Lean.MVarId",
"Lean.Expr",
"Lean.FVarId",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Expr.sort",
"Lean.Expr.bvar",
"Lean.Level",
"Lean.Literal",
"Lean.Expr.mdata",
"Lean.Expr.fvar",
"Lean.... | false |
Mathlib.Tactic.DefEqAbuse._aux_Mathlib_Tactic_DefEqAbuse___elabRules_Mathlib_Tactic_DefEqAbuse_defeqAbuse_1 | Mathlib.Tactic.DefEqAbuse | [
"Pure.pure",
"Lean.Core.instMonadTraceCoreM",
"Lean.TSyntax",
"Lean.Elab.Tactic.instMonadExceptExceptionTacticM",
"Lean.MessageData",
"Unit.unit",
"Lean.Exception.internal",
"Lean.instMonadExceptOfExceptionCoreM",
"Std.instToFormatString",
"Array.mkEmpty",
"Except.ok",
"Lean.PersistentArrayNod... | false |
_private.Lean.Elab.DeclModifiers.0.Lean.Elab.Modifiers.isNoncomputable._sparseCasesOn_1 | Lean.Elab.DeclModifiers | [
"Nat.ne_of_beq_eq_false",
"Lean.Elab.ComputeKind",
"Lean.Elab.ComputeKind.ctorIdx",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Elab.ComputeKind.noncomputable",
"Nat.land",
"Lean.Elab.ComputeKind.meta",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"Lean.Elab.Comput... | false |
_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital.0._auto_85 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
MeasureTheory.Measure.addHaarMeasure.eq_1 | Mathlib.MeasureTheory.Measure.Haar.Basic | [
"instHSMul",
"MeasureTheory.Measure",
"TopologicalSpace.PositiveCompacts.instSetLike",
"CommSemiring.toSemiring",
"Algebra.toSMul",
"BorelSpace",
"Algebra.id",
"MeasureTheory.Measure.instSMul",
"ENNReal.instCommSemiring",
"MeasureTheory.Measure.addHaarMeasure._proof_1",
"MeasurableSpace",
"Top... | true |
CategoryTheory.Functor.HomObj.naturality_assoc | Mathlib.CategoryTheory.Functor.FunctorHom | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Eq.mp",
"id",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"CategoryTheory.Functor.map",
"CategoryTheory.Functor.HomObj.app",
"congr",
"CategoryTheory.types",
"CategoryThe... | true |
Lean.Meta.getElimExprInfo | Lean.Meta.Tactic.ElimInfo | [
"Pure.pure",
"Lean.Core.instMonadTraceCoreM",
"Array.takeWhile",
"Std.Rci.mk",
"Lean.MessageData",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"bne",
"Subarray",
"Bool.not",
"Std.Rio.instForIn'InferInstanceMembershipOfLawfulUpwardEnumerableOfLawfulUpwardEnumerableLTOfLawfulUpwa... | true |
CategoryTheory.ShortComplex.RightHomologyMapData.compatibilityOfZerosOfIsColimitCokernelCofork._proof_3 | Mathlib.Algebra.Homology.ShortComplex.RightHomology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex.RightHomologyData.ofZeros",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"congrArg",
"CategoryTheory.Limits.CokernelCofork",
"CategoryTheory.ShortComplex",
"CategoryTheory.S... | false |
_private.Mathlib.Analysis.BoxIntegral.Box.Basic.0.BoxIntegral.Box.disjoint_withBotCoe._simp_1_1 | Mathlib.Analysis.BoxIntegral.Box.Basic | [
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"OrderBot",
"SemilatticeInf.toPartialOrder",
"Bot.bot",
"SemilatticeInf.toMin",
"LE.le",
"SemilatticeInf",
"propext",
"disjoint_iff_inf_le",
"Eq",
"Min.min"
] | false |
TopologicalSpace.IrreducibleCloseds.mk.injEq | Mathlib.Topology.Sets.Closeds | [
"Eq.propIntro",
"IsIrreducible",
"TopologicalSpace.IrreducibleCloseds",
"IsClosed",
"TopologicalSpace",
"Eq.ndrec",
"TopologicalSpace.IrreducibleCloseds.mk.inj",
"Eq.refl",
"Eq",
"TopologicalSpace.IrreducibleCloseds.mk",
"Set"
] | true |
TopologicalSpace.IsTopologicalBasis.nhds_hasBasis | Mathlib.Topology.Bases | [
"Filter.instMembership",
"congrArg",
"Membership.mem",
"Exists",
"nhds",
"HasSubset.Subset",
"iff_self",
"TopologicalSpace",
"funext",
"And",
"Filter.HasBasis",
"Iff",
"Filter.HasBasis.mk",
"True",
"TopologicalSpace.IsTopologicalBasis",
"Iff.trans",
"of_eq_true",
"TopologicalSpace.... | true |
Int.divisorsAntidiag_neg_natCast._proof_1 | Mathlib.NumberTheory.Divisors | [
"not_exists._simp_1",
"NegZeroClass.toNeg",
"False",
"Int.instIsStrictOrderedRing",
"Nat.instMulZeroClass",
"IsDomain.to_noZeroDivisors",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"Nat.divisorsAntidiagonal",
"eq_false",
"congrArg",
"and_sel... | false |
AddMonoidHom.compHom'_apply_apply | Mathlib.Algebra.Group.Hom.Instances | [
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddMonoidHom.instAddCommMonoid",
"AddMonoidHom.compHom'",
"AddCommMonoid",
"AddZeroClass",
"Eq.refl",
"AddCommMonoid.toAddMonoid",
"AddMonoidHom",
"AddMonoidHom.instFunLike",
"Eq",
"DFunLike.coe"
] | true |
Lean.MetavarContext.incDepth | Lean.MetavarContext | [
"Lean.MetavarContext.decls",
"Lean.MetavarContext.lDepth",
"Lean.MetavarContext.eAssignment",
"Lean.MetavarContext.mvarCounter",
"Lean.MetavarContext.mk",
"Lean.MetavarContext",
"Lean.MetavarContext.depth",
"Lean.MetavarContext.levelAssignDepth",
"instDecidableEqBool",
"instOfNatNat",
"Bool.true... | true |
Matrix.circulant_col_zero_eq | Mathlib.LinearAlgebra.Matrix.Circulant | [
"sub_zero",
"HSub.hSub",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubtractionMonoid.toSubNegMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"congr_arg",
"SubNegMonoid.toSub",
"instHSub",
"SubtractionMonoid",
"Zero.toOfNat0",
"OfNat.ofNat",
"NegZeroClass.toZero",
"Eq",
"Matrix.circulant"
] | true |
CategoryTheory.toSkeleton | Mathlib.CategoryTheory.Skeletal | [
"CategoryTheory.isIsomorphicSetoid",
"Quotient.mk",
"CategoryTheory.Category",
"CategoryTheory.Skeleton"
] | true |
Homotopy.mkInductiveAux₂._proof_4 | Mathlib.Algebra.Homology.Homotopy | [
"PSigma.snd",
"HomologicalComplex.xNext",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"ChainComplex",
"HomologicalComplex.instCategory",
"Nat.instOne",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"AddRightCanc... | false |
Ideal.radical_le_jacobson | Mathlib.RingTheory.Jacobson.Ideal | [
"CommRing",
"Semiring.toModule",
"CommSemiring.toSemiring",
"Submodule.completeLattice",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"Membership.mem",
"Eq.rec",
"Ideal.jacobson",
"Submodule.instPartialOrder",
"LE.le",
"Ideal.IsMaximal.isPrime",
"Ideal",
"Ideal.radical_eq_sInf",
... | true |
Lean.DataValue.ofString.injEq | Lean.Data.KVMap | [
"Eq.propIntro",
"String",
"Lean.DataValue.ofString.inj",
"Lean.DataValue.ofString",
"Eq.ndrec",
"Eq.refl",
"Lean.DataValue",
"Eq"
] | true |
Lean.Elab.Term.PostponeBehavior.partial.sizeOf_spec | Lean.Elab.SyntheticMVars | [
"Lean.Elab.Term.PostponeBehavior",
"Lean.Elab.Term.PostponeBehavior._sizeOf_inst",
"instOfNatNat",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"Lean.Elab.Term.PostponeBehavior.partial"
] | true |
_private.Batteries.Data.List.Perm.0.List.Perm.idxBij_leftInverse_idxBij_symm._proof_1_15 | Batteries.Data.List.Perm | [
"Lean.Grind.nestedProof",
"Lean.Grind.Nat.lt_eq",
"LawfulBEq",
"List.Perm",
"instOfNatNat",
"LE.le",
"instLENat",
"Fin.val",
"GetElem.getElem",
"List.getElem_filter_eq_getElem_getElem_findIdxs._proof_5",
"List.findIdxs",
"List",
"instHAdd",
"BEq.beq",
"_private.Batteries.Data.List.Perm.0... | false |
AddCommGrpCat.instCreatesColimitsOfSizeUliftFunctor | Mathlib.Algebra.Category.Grp.Ulift | [
"CategoryTheory.CreatesColimitsOfShape.mk",
"CategoryTheory.Functor",
"AddCommGrpCat.uliftFunctor",
"AddCommGrpCat.instCategory",
"AddCommGrpCat.instFaithfulUliftFunctor",
"CategoryTheory.CreatesColimitsOfSize.mk",
"AddCommGrpCat.instCreatesColimitsOfSizeUliftFunctor._proof_1",
"CategoryTheory.reflect... | true |
FloorRing.ofFloor._proof_1 | Mathlib.Algebra.Order.Floor.Defs | [
"AddGroup.toSubtractionMonoid",
"Int.cast_neg",
"Int.cast",
"Eq.mpr",
"NegZeroClass.toNeg",
"neg_le",
"Ring.toNonAssocRing",
"AddGroupWithOne.toAddGroup",
"congrArg",
"LinearOrder",
"covariant_swap_add_of_covariant_add",
"Iff.rfl",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"Preor... | false |
Units.coe_smul | Mathlib.Algebra.Group.Action.Units | [
"Monoid",
"Units.val",
"instHSMul",
"Units",
"Monoid.toSemigroup",
"MulDistribMulAction.toMulAction",
"HSMul.hSMul",
"SemigroupAction.toSMul",
"MulAction.toSemigroupAction",
"Units.mulDistribMulActionRight",
"MulDistribMulAction",
"Eq",
"Units.instMonoid",
"rfl"
] | true |
_private.Lean.Meta.ExprDefEq.0.Lean.Meta.processAssignmentFOApproxAux | Lean.Meta.ExprDefEq | [
"Pure.pure",
"Lean.Expr.brecOn",
"_private.Lean.Meta.ExprDefEq.0.Lean.Meta.processAssignmentFOApproxAux.match_1",
"Lean.Meta.State",
"HSub.hSub",
"Array.isEmpty",
"Lean.mkAppRange",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"instDecidableEqBool",
"Lean.Meta.isExprDefEqAux",
"instSubNat... | true |
UpperHalfPlane.measurableEmbedding_coe | Mathlib.Analysis.Complex.UpperHalfPlane.Measure | [
"NormedCommRing.toSeminormedCommRing",
"UpperHalfPlane.instMeasurableSpace",
"UpperHalfPlane.isOpenEmbedding_coe",
"Complex.borelSpace",
"UpperHalfPlane.coe",
"Complex.instNormedField",
"PseudoMetricSpace.toUniformSpace",
"Complex.measurableSpace",
"Topology.IsOpenEmbedding.measurableEmbedding",
"... | true |
_private.Lean.Elab.Extra.0.Lean.Elab.Term.Op.applyCoe | Lean.Elab.Extra | [
"Inhabited.default",
"Lean.Elab.Term.instInhabitedTermElabM",
"Lean.Expr",
"Lean.Elab.Term.TermElabM",
"Bool",
"_private.Lean.Elab.Extra.0.Lean.Elab.Term.Op.Tree"
] | true |
Nat.lt_sum_ge | Batteries.Data.Nat.Lemmas | [
"PSum",
"PSum.inr",
"LE.le",
"instLENat",
"dite",
"PSum.inl",
"Nat",
"LT.lt",
"Nat.lt_sum_ge._proof_1",
"Nat.decLt",
"instLTNat",
"Not"
] | true |
CategoryTheory.ShortComplex.SnakeInput.functorL₃_obj | Mathlib.Algebra.Homology.ShortComplex.SnakeLemma | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.ShortComplex.SnakeInput.L₃",
"CategoryTheory.ShortComplex.SnakeInput.functorL₃",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.SnakeInput",
"CategoryTheory.Abelian",
"CategoryTheory.ShortComplex.instCategory",
"CategoryTheory.ShortC... | true |
_private.Lean.Meta.Tactic.Grind.EMatchTheorem.0.Lean.Meta.Grind.mkEMatchTheoremAndSuggest.match_5 | Lean.Meta.Tactic.Grind.EMatchTheorem | [
"_private.Lean.Meta.Tactic.Grind.EMatchTheorem.0.Lean.Meta.Grind.SelectM.State",
"Prod.mk",
"Unit",
"Prod",
"Prod.casesOn"
] | false |
CircleDeg1Lift.monotone | Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber | [
"Real",
"Monotone",
"CircleDeg1Lift.instFunLikeReal",
"CircleDeg1Lift.toOrderHom",
"DFunLike.coe",
"CircleDeg1Lift",
"Real.instPreorder",
"OrderHom.monotone'"
] | true |
CategoryTheory.Pretriangulated.Triangle.functorHomMk._proof_1 | Mathlib.CategoryTheory.Triangulated.Basic | [
"CategoryTheory.Pretriangulated.Triangle.π₃",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.shiftFunctor",
"CategoryTheory.Functor.whiskerLeft",
"CategoryTheory.Pretriangulated.Trian... | false |
Ideal.map_pi | Mathlib.RingTheory.Ideal.Quotient.Basic | [
"Eq.mpr",
"Pi.Function.module",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"Semiring.toModule",
"instSMulOfMul",
"Pi.addCommMonoid",
"SemilinearMapClass.toMulActionSemiHomClass",
"HMul.hMul",
"Finset.univ",
"SemilinearMapClass.distribMulActionSemiHomClass",
"Ring.toNonAssocRing",
... | true |
ENat.pow_ne_top_iff | Mathlib.Data.ENat.Basic | [
"IsDomain.to_noZeroDivisors",
"instTopENat",
"Nat.instNontrivial",
"CommSemiring.toSemiring",
"Nat.instIsDomain",
"Ne",
"instOfNatNat",
"Monoid.toPow",
"Nat.instMonoidWithZero",
"Iff",
"HPow.hPow",
"Nat",
"ENat",
"instCommSemiringENat",
"Nat.instSemiring",
"instDecidableEqNat",
"Or",... | true |
Nat.count_strict_mono | Mathlib.Data.Nat.Count | [
"Iff.mpr",
"instOfNatNat",
"LE.le",
"Nat.count_monotone",
"instLENat",
"instHAdd",
"HAdd.hAdd",
"Nat.instPreorder",
"LT.lt.trans_le",
"DecidablePred",
"Nat",
"LT.lt",
"Nat.count",
"Nat.count_lt_count_succ_iff",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"Nat.succ_le_iff",
"Nat.suc... | true |
DirectSum.lequivCongrLeft_symm_lof | Mathlib.Algebra.DirectSum.Module | [
"DirectSum.lequivCongrLeft",
"Eq.mpr",
"LinearEquiv.symm",
"Equiv.instEquivLike",
"instAddCommMonoidDirectSum",
"DirectSum.instModule",
"congrArg",
"LinearEquiv.symm_apply_eq",
"LinearMap.instFunLike",
"cast",
"id",
"Equiv",
"LinearMap",
"AddCommMonoid",
"RingHomInvPair.ids",
"DirectSu... | true |
Function.Embedding.twoEmbeddingEquiv.match_1 | Mathlib.Data.Fin.Tuple.Embedding | [
"Prod.mk",
"Prod",
"Prod.casesOn"
] | false |
EMetric.ball_subset | Mathlib.Topology.EMetricSpace.Defs | [
"CommSemiring.toSemiring",
"PartialOrder.toPreorder",
"Metric.eball_subset",
"Preorder.toLE",
"Distrib.toAdd",
"HasSubset.Subset",
"Ne",
"ENNReal.instCommSemiring",
"LE.le",
"Metric.eball",
"PseudoEMetricSpace",
"instHAdd",
"PseudoEMetricSpace.toEDist",
"HAdd.hAdd",
"NonAssocSemiring.toN... | true |
_private.Mathlib.NumberTheory.Padics.ProperSpace.0.PadicInt.totallyBounded_univ._simp_1_5 | Mathlib.NumberTheory.Padics.ProperSpace | [
"Membership.mem",
"Exists",
"And",
"propext",
"Set.image",
"Set.exists_mem_image",
"Eq",
"Set.instMembership",
"Set"
] | false |
_private.Mathlib.Tactic.NormNum.Eq.0.Mathlib.Meta.NormNum.evalEq.match_8 | Mathlib.Tactic.NormNum.Eq | [
"Option.ctorIdx",
"Lean.Expr.const",
"Option.some",
"_private.Mathlib.Tactic.NormNum.Eq.0.Mathlib.Meta.NormNum.evalEq._sparseCasesOn_3",
"Nat.hasNotBit",
"Lean.Expr.sort",
"Lean.Level",
"List.cons",
"Qq.Quoted",
"Lean.Name.mkStr2",
"Lean.Expr.app",
"Lean.Level.succ",
"Lean.Name.mkStr1",
"L... | false |
CochainComplex.Lifting.coe_cocycle₁'_v_comp_eq_zero | Mathlib.Algebra.Homology.ModelCategory.Lifting | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Category.assoc",
"CochainComplex.Lifting.cochain₀._proof_1",
"HomologicalComplex.instCategory",
"CochainComplex.HomComplex.instAddCommGroupCochain",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"sub_self",... | true |
Vector.findSomeRev? | Init.Data.Vector.Basic | [
"Vector",
"Array.findSomeRev?",
"Nat",
"Vector.toArray",
"Option"
] | true |
_private.Mathlib.Order.Interval.Finset.Nat.0.Nat.Ico_succ_left_eq_erase_Ico._simp_1_2 | Mathlib.Order.Interval.Finset.Nat | [
"Preorder.toLT",
"Finset",
"Preorder.toLE",
"Membership.mem",
"Finset.Ico",
"LE.le",
"And",
"Finset.instSetLike",
"LT.lt",
"propext",
"LocallyFiniteOrder",
"Eq",
"SetLike.instMembership",
"Preorder",
"Finset.mem_Ico"
] | false |
ProofWidgets.RpcEncodablePacket.mk.injEq._@.ProofWidgets.Presentation.Expr.3227936355._hygCtx._hyg.1 | ProofWidgets.Presentation.Expr | [
"Lean.Json",
"Eq.propIntro",
"ProofWidgets.RpcEncodablePacket.mk.inj._@.ProofWidgets.Presentation.Expr.3227936355._hygCtx._hyg.1",
"ProofWidgets.RpcEncodablePacket.mk._@.ProofWidgets.Presentation.Expr.3227936355._hygCtx._hyg.1",
"ProofWidgets.RpcEncodablePacket._@.ProofWidgets.Presentation.Expr.3227936355._... | false |
_private.Mathlib.Topology.Algebra.Module.PointwiseConvergence.0.PointwiseConvergenceCLM.tendsto_iff_forall_tendsto._simp_1_1 | Mathlib.Topology.Algebra.Module.PointwiseConvergence | [
"Pi.topologicalSpace",
"nhds",
"tendsto_pi_nhds",
"TopologicalSpace",
"Filter.Tendsto",
"propext",
"Eq",
"Filter"
] | false |
HasSum.smul_eq | Mathlib.Topology.Algebra.InfiniteSum.Module | [
"instHSMul",
"ContinuousSMul",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"HasSum.prod_fiberwise",
"SummationFilter.instNeBotUnconditional",
"Prod.fst",
"AddCommMonoid",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"To... | true |
NormedStarGroup.rec | Mathlib.Analysis.CStarAlgebra.Basic | [
"NormedStarGroup.mk",
"Norm.norm",
"Real.instLE",
"Real",
"SeminormedAddGroup.toAddGroup",
"SeminormedAddCommGroup",
"LE.le",
"StarAddMonoid.toInvolutiveStar",
"NormedStarGroup",
"SeminormedAddCommGroup.toSeminormedAddGroup",
"SeminormedAddCommGroup.toNorm",
"AddGroup.toSubNegMonoid",
"StarA... | false |
HomotopicalAlgebra.Precylinder.mk.inj | Mathlib.AlgebraicTopology.ModelCategory.Cylinder | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomotopicalAlgebra.Precylinder.i₀_π._autoParam",
"CategoryTheory.CategoryStruct.id",
"HomotopicalAlgebra.Precylinder.i₁_π._autoParam",
"autoParam",
"HomotopicalAlgebra.Precylinder.mk.noConfusion",
"HomotopicalAlgebra.Precylinder",
"Homotopical... | true |
HasCardinalLT.Set.cocone_ι_app | Mathlib.CategoryTheory.Presentable.Type | [
"CategoryTheory.Functor",
"HasCardinalLT",
"CompleteLattice.instOmegaCompletePartialOrder",
"Cardinal",
"HasCardinalLT.Set.functor",
"HasCardinalLT.Set.functor._proof_1",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"Membership.mem",
"Set.Elem",
"Subtype",
"HasCardinalLT.Set.c... | true |
Equiv.prodUnique_symm_apply | Mathlib.Logic.Equiv.Prod | [
"Inhabited.default",
"Equiv.instEquivLike",
"Unique",
"Equiv",
"Prod.mk",
"Equiv.prodUnique",
"Unique.instInhabited",
"Equiv.symm",
"Prod",
"Eq",
"DFunLike.coe",
"rfl",
"EquivLike.toFunLike"
] | true |
MeasureTheory.Measure.sum_eq_zero | Mathlib.MeasureTheory.Measure.MeasureSpace | [
"MeasureTheory.Measure",
"MeasurableSet",
"ENNReal.instAddCommMonoid",
"congrArg",
"forall_comm",
"MeasureTheory.Measure.sum_apply",
"MeasureTheory.Measure.instZero",
"instZeroENNReal",
"iff_self",
"MeasurableSpace",
"Iff",
"tsum",
"congr",
"True",
"ENNReal",
"propext",
"of_eq_true",... | true |
Turing.PartrecToTM2.natEnd | Mathlib.Computability.TuringMachine.ToPartrec | [
"Turing.PartrecToTM2.Γ'",
"Turing.PartrecToTM2.natEnd.match_1",
"Bool.true",
"Unit",
"Bool",
"Bool.false"
] | true |
Lean.addTraceAsMessages | Lean.Util.Trace | [
"Pure.pure",
"Lean.MessageData",
"String.instLTRaw",
"Lean.PersistentArray.instForInOfMonad",
"Lean.Elab.mkMessageCore",
"Lean.TraceResult",
"Lean.MonadRef.getRef",
"instHashableProd",
"Array.push",
"Lean.MonadTrace",
"instForInOfForIn'",
"Lean.replaceRef",
"Monad.toApplicative",
"Lean.Syn... | true |
Real.exp_one_rpow | Mathlib.Analysis.SpecialFunctions.Pow.Real | [
"Eq.mpr",
"MulOne.toOne",
"Real.instPow",
"Real.exp_mul",
"Real",
"HMul.hMul",
"congrArg",
"Real.semiring",
"id",
"MulOne.toMul",
"NonAssocSemiring.toMulZeroOneClass",
"Real.exp",
"MulZeroOneClass.toMulOneClass",
"Real.instOne",
"MulOneClass.toMulOne",
"HPow.hPow",
"Real.instMul",
... | true |
CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv' | Mathlib.CategoryTheory.Limits.Presheaf | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"Opposite",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Comma.left",
"CategoryTheory.Functor.comp",
"CategoryTheory.yoneda",
... | true |
AddCon.pi.eq_1 | Mathlib.GroupTheory.Congruence.Basic | [
"AddCon",
"piSetoid",
"AddCon.pi",
"AddCon.toSetoid",
"Pi.instAdd",
"Eq.refl",
"AddCon.pi._proof_1",
"AddCon.mk",
"Eq",
"Add"
] | true |
CategoryTheory.ShortComplex.Homotopy.rec | Mathlib.Algebra.Homology.ShortComplex.Preadditive | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex.Hom.τ₁",
"AddCommGroup.toAddCommMonoid",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.X₁",
"CategoryTheory.ShortComplex.Homotopy",
"CategoryTheory.ShortComplex.instCategory",
"CategoryTheory.ShortComp... | false |
PEquiv.injective_of_forall_isSome | Mathlib.Data.PEquiv | [
"PEquiv.instFunLikeOption",
"False.elim",
"PEquiv.injective_of_forall_ne_isSome",
"Classical.choice",
"Ne",
"Nonempty.intro",
"Bool.true",
"Classical.em",
"Bool",
"Nonempty",
"Function.Injective",
"PEquiv",
"Option.isSome",
"Or.elim",
"Eq",
"DFunLike.coe",
"Not",
"Option"
] | true |
CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.commMonToLaxBraidedObj_ε | Mathlib.CategoryTheory.Monoidal.CommMon_ | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"PUnit.addCommGroup",
"CategoryTheory.Functor.LaxMonoidal.ε",
"AddCommGroup.toAddGroup",
"CategoryTheory.BraidedCategory",
"CategoryTheory.MonObj.one",
"CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.commM... | true |
List.sum | Init.Data.List.Basic | [
"List",
"instHAdd",
"HAdd.hAdd",
"Zero.toOfNat0",
"OfNat.ofNat",
"List.foldr",
"Add",
"Zero"
] | true |
HomotopyGroup.commGroup._proof_2 | Mathlib.Topology.Homotopy.HomotopyGroup | [
"Nontrivial",
"Exists",
"exists_ne",
"Ne",
"Nontrivial.to_nonempty",
"Classical.arbitrary"
] | false |
Set.Finite.induction_on_subset | Mathlib.Data.Set.Finite.Basic | [
"Set.finite_empty",
"congrArg",
"Set.Finite",
"Membership.mem",
"Eq.mp",
"Insert.insert",
"HasSubset.Subset",
"Set.Finite.subset",
"Set.insert_subset_iff",
"And",
"Set.Finite.induction_on",
"Set.Subset.rfl",
"Set.instInsert",
"And.right",
"And.left",
"propext",
"Set.instEmptyCollecti... | true |
Lean.Meta.Simp.Result.mk.noConfusion | Lean.Meta.Tactic.Simp.Types | [
"Lean.Meta.Simp.Result.mk",
"Lean.Expr",
"id",
"Lean.Meta.Simp.Result",
"Bool",
"Eq",
"Lean.Meta.Simp.Result.noConfusion",
"Option"
] | false |
_private.Init.Data.String.Lemmas.Iterate.0.String.Model.revPositionsFrom._proof_1 | Init.Data.String.Lemmas.Iterate | [
"String.Pos.Down",
"String",
"invImage",
"String.Pos.down",
"Lean.opaqueId",
"String.Pos",
"String.Pos.instWellFoundedRelationDown",
"WellFounded"
] | false |
_private.Lean.ImportingFlag.0.Lean.initFn._@.Lean.ImportingFlag.2251799370._hygCtx._hyg.2 | Lean.ImportingFlag | [
"IO.mkRef",
"instMonadLiftT",
"IO",
"EIO",
"liftM",
"Bool",
"IO.Error",
"IO.Ref",
"instMonadLiftTOfMonadLift",
"Bool.false",
"BaseIO",
"instMonadLiftBaseIOEIO"
] | false |
CategoryTheory.MonObj.one_associator | Mathlib.CategoryTheory.Monoidal.Mon_ | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory.id_whiskerLeft",
"CategoryTheory.MonoidalCategory.id_tensorHom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"... | true |
Array.reverse_zipWith | Init.Data.Array.Zip | [
"List.zipWith",
"Array.reverse",
"congrArg",
"List.reverse_toArray",
"Eq.mp",
"Array.casesOn",
"List.toArray",
"Array",
"List",
"List.size_toArray",
"Nat",
"congr",
"True",
"eq_self",
"List.reverse",
"of_eq_true",
"Eq.ndrec",
"List.zipWith_toArray",
"Eq.refl",
"Array.mk",
"Eq... | true |
LinearPMap.inverse_apply_eq | Mathlib.LinearAlgebra.LinearPMap | [
"Submodule",
"LinearPMap.inverse",
"LinearPMap.mem_inverse_graph",
"AddCommGroup.toAddCommMonoid",
"Submodule.addCommMonoid",
"LinearMap.ker",
"Membership.mem",
"AddCommGroup",
"Subtype",
"Prod.mk",
"Bot.bot",
"Submodule.module",
"Submodule.instBot",
"LinearPMap",
"LinearPMap.toFun",
"... | true |
Lean.MonadCache.noConfusionType | Lean.Util.MonadCache | [
"Lean.MonadCache.casesOn",
"Unit",
"Lean.MonadCache",
"HEq",
"Option"
] | false |
Lean.Parser.Command.versoCommentBody.parenthesizer | Lean.Parser.Term | [
"Lean.PrettyPrinter.Parenthesizer",
"Lean.PrettyPrinter.Parenthesizer.visitToken"
] | true |
Polynomial.resultant_add_mul_right | Mathlib.RingTheory.Polynomial.Resultant.Basic | [
"Distrib.leftDistribClass",
"Eq.mpr",
"CommRing",
"Nat.recAux",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Polynomial.le_natDegree_of_mem_supp",
"Semiring.toModule",
"le_rfl",
"HMul.hMul",
"Polynomial.resultant",
"CommRing.toNonUnitalCommRing",
"AddMonoid.toAddSemigroup",
"MulZeroClas... | true |
CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan._proof_7 | Mathlib.CategoryTheory.Limits.Constructions.Over.Products | [
"CategoryTheory.instCategoryUnder",
"CategoryTheory.Limits.WalkingSpan",
"CategoryTheory.Comma.right",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Under.homMk",
"CategoryTheory.Limits.PushoutCocone.condition",
"CategoryTheory.Limits.CoconeMorphism.hom",
"CategoryTheory.Co... | false |
_private.Init.Data.Iterators.Consumers.Access.0.Std.Iter.atIdxSlow?.match_3.eq_2 | Init.Data.Iterators.Consumers.Access | [
"Std.IterStep",
"Std.IterStep.skip",
"Id",
"Std.Iterator",
"Subtype.mk",
"Std.Iter",
"Std.IterStep.yield",
"Std.Iter.atIdxSlow?.match_3",
"Std.Iter.IsPlausibleStep",
"Std.IterStep.done",
"Eq.refl",
"Eq",
"Std.Iter.Step"
] | true |
_private.Init.Data.Order.FactoriesExtra.0.DecidableLE.ofOrd._simp_3 | Init.Data.Order.FactoriesExtra | [
"Std.LawfulOrderOrd",
"Ord",
"LE.le",
"Ord.compare",
"LE",
"Bool.true",
"propext",
"Bool",
"Std.LawfulOrderOrd.isLE_compare",
"Ordering.isLE",
"Eq"
] | false |
Subgroup.coe_subgroupOf | Mathlib.Algebra.Group.Subgroup.Map | [
"Subgroup.subgroupOf",
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"Subgroup.subtype",
"Group",
"Membership.mem",
"Subtype",
"DivInvMonoid.toMonoid",
"Subgroup",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"SetLike.coe",
"Set.preimage",
"Subgroup.toGroup",
"Eq",
... | true |
ProfiniteGrp.ProfiniteCompletion.adjunction._proof_2 | Mathlib.Topology.Algebra.Category.ProfiniteGrp.Completion | [
"GrpCat.instConcreteCategoryMonoidHomCarrier",
"CategoryTheory.Category.assoc",
"ProfiniteGrp.ProfiniteCompletion.lift_eta",
"GrpCat",
"MonoidHom.instFunLike",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"GrpCat.str",
"ProfiniteGrp.ProfiniteComplet... | false |
NonUnitalStarSubalgebra.coe_add | Mathlib.Algebra.Star.NonUnitalSubalgebra | [
"CommSemiring.toSemiring",
"Membership.mem",
"Subtype",
"Distrib.toAdd",
"CommSemiring",
"NonUnitalStarSubalgebra.instNonUnitalSubsemiringClass",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonUnitalStarSubalgebra.instSetLike",
"instHAdd",
"HAdd.hAdd",
"Star",
"NonUnitalNonAssocSemiring.toDi... | true |
inv_add_inv | Mathlib.Algebra.Field.Basic | [
"instHDiv",
"HMul.hMul",
"GroupWithZero.toDivInvMonoid",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"CommSemiring.toNonUnitalCommSemiring",
"DivisionSemiring.toGroupWithZero",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"DivisionMonoid.toDivInvOneMonoid",
"Semifield",
... | true |
IsDedekindDomain.HeightOneSpectrum.instAlgebraSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers._proof_6 | Mathlib.RingTheory.DedekindDomain.AdicValuation | [
"Int.instAddCommGroup",
"IsDedekindDomain.HeightOneSpectrum.instAlgebraSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers._proof_2",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Eq.mpr",
"UniformSpace.Completion.coe'",
"Multiplicative.linearOrder",
"MulOne.toOne",
"CommRin... | false |
Polynomial.shiftedLegendre | Mathlib.RingTheory.Polynomial.ShiftedLegendre | [
"Polynomial.C",
"Nat.choose",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"RingHom",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Int.instNegInt",
"instOfNatNat",
"Int",
"Nat.cast",
"Polynomial",
"Int.instMonoid",
"Monoid.toPow",
... | true |
ENat.top_sub_one | Mathlib.Data.ENat.Basic | [
"instAddMonoidWithOneENat",
"instTopENat",
"instSubENat",
"HSub.hSub",
"AddMonoidWithOne.toOne",
"instHSub",
"ENat",
"One.toOfNat1",
"Top.top",
"OfNat.ofNat",
"Eq",
"rfl"
] | true |
KaehlerDifferential.derivationQuotKerTotal._proof_5 | Mathlib.RingTheory.Kaehler.Basic | [
"Submodule",
"Submodule.Quotient.instZeroQuotient",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Finsupp.module",
"CommRing.toNonUnitalCommRing",
"Submodule.Quotient.addCommGroup",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"AddGroupWithOne.t... | false |
AlgebraicGeometry.IsClosedImmersion.comp_iff | Mathlib.AlgebraicGeometry.Morphisms.Separated | [
"AlgebraicGeometry.Scheme",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AlgebraicGeometry.IsClosedImmersion.comp",
"AlgebraicGeometry.IsSeparated.isSeparated_of_mono",
"inferInstance",
"AlgebraicGeometry.IsPreimmersion.instMonoScheme",
"Iff",
"AlgebraicGeometry.IsClosedImmersion.instIsP... | true |
AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal._proof_1 | Mathlib.AlgebraicGeometry.IdealSheaf.Basic | [
"AlgebraicGeometry.Scheme",
"Membership.mem",
"Set.Elem",
"AlgebraicGeometry.Scheme.affineOpens",
"Subtype.val",
"Set.instMembership",
"AlgebraicGeometry.Scheme.Opens",
"Subtype.property",
"Set"
] | false |
ContDiffMapSupportedIn.coe_of_support_subset | Mathlib.Analysis.Distribution.ContDiffMapSupportedIn | [
"Real",
"ContDiffMapSupportedIn.of_support_subset",
"NormedSpace",
"Real.denselyNormedField",
"PseudoMetricSpace.toUniformSpace",
"ContDiff",
"HasSubset.Subset",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"ContDiffMapSupportedIn.toContDiffMapSupportedInClass",
"Su... | true |
MulActionHom.instCoeTCOfMulActionSemiHomClass.eq_1 | Mathlib.GroupTheory.GroupAction.Hom | [
"CoeTC",
"SMul",
"MulActionSemiHomClass",
"MulActionHom.instCoeTCOfMulActionSemiHomClass",
"MulActionSemiHomClass.toMulActionHom",
"Eq.refl",
"MulActionHom",
"Eq",
"FunLike",
"CoeTC.mk"
] | true |
Bundle.Trivialization.zeroSection | Mathlib.Topology.VectorBundle.Basic | [
"Eq.mpr",
"Bundle.Trivialization.toFun'",
"SemilinearMapClass.distribMulActionSemiHomClass",
"NormedSpace",
"FiberBundle",
"congrArg",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUniformSpace",
"RingHom",
"Membership.mem",
"NormedField.toField",
"Bundle.TotalSpac... | true |
AddAction.fixedPoints | Mathlib.GroupTheory.GroupAction.Defs | [
"AddMonoid.toAddSemigroup",
"setOf",
"HVAdd.hVAdd",
"AddAction",
"AddAction.toAddSemigroupAction",
"AddSemigroupAction.toVAdd",
"AddMonoid",
"instHVAdd",
"Eq",
"Set"
] | true |
finite_mulSupport_of_finprod_ne_one | Mathlib.Algebra.BigOperators.Finprod | [
"MulOne.toOne",
"Monoid.toMulOneClass",
"hasFiniteMulSupport_of_finprod_ne_one",
"Ne",
"MulOneClass.toMulOne",
"finprod",
"CommMonoid.toMonoid",
"One.toOfNat1",
"Function.HasFiniteMulSupport",
"OfNat.ofNat",
"CommMonoid"
] | true |
Lean.Meta.Grind.Arith.Cutsat.EqCnstrProof.pow.inj | Lean.Meta.Tactic.Grind.Arith.Cutsat.Types | [
"Lean.Meta.Grind.Arith.Cutsat.EqCnstrProof.pow",
"Int",
"And",
"Nat",
"And.intro",
"Lean.Meta.Grind.Arith.Cutsat.EqCnstrProof",
"Lean.Meta.Grind.Arith.Cutsat.EqCnstrProof.pow.noConfusion",
"Eq",
"Lean.Meta.Grind.Arith.Cutsat.EqCnstr",
"Option"
] | true |
Mathlib.Tactic.ModCases.IntMod.proveOnModCases | Mathlib.Tactic.ModCases | [
"Inhabited.default",
"Lean.Expr.const",
"Lean.Name.mkStr5",
"Lean.MVarId",
"Lean.Meta.MetaM",
"Lean.Expr.sort",
"Lean.Level",
"List.cons",
"List",
"Qq.Quoted",
"Lean.Meta.instInhabitedMetaM",
"Lean.Expr.app",
"Prod",
"Lean.Name.mkStr1",
"List.nil"
] | true |
NormedAddCommGroup.toSeminormedAddCommGroup | Mathlib.Analysis.Normed.Group.Defs | [
"SeminormedAddCommGroup",
"NormedAddCommGroup.toMetricSpace",
"NormedAddCommGroup.dist_eq",
"NormedAddCommGroup.toNorm",
"NormedAddCommGroup.toAddCommGroup",
"MetricSpace.toPseudoMetricSpace",
"SeminormedAddCommGroup.mk",
"NormedAddCommGroup"
] | true |
PadicInt.modPart | Mathlib.NumberTheory.Padics.RingHoms | [
"Rat.num",
"HMul.hMul",
"Rat",
"Rat.den",
"instHMod",
"Int",
"Nat.cast",
"Int.instMul",
"HMod.hMod",
"Nat",
"Nat.gcdA",
"Int.instMod",
"instNatCastInt",
"instHMul"
] | true |
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